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1 year ago

3 + 5.2x= 1 - 2.8x how do I solve this?

1 answer:

5 0

3+5.2x=1-2.8x

1. 3+5.2x+2.8x=1

2. 5.2x+2.8x=1-3

5.2x+2.8x=1-3

1. 8x=1-3

2. 8x=-2

8x=-2

1. =-(1/4)

Alternative form:

2. x=-0.25

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Caleb bought groceries and paid $1.60 in sales tax.the sales tax rate is 2.5% What was the price of Caleb’s groceries,before tax

Goryan [66]

Let price of the Caleb's groceries was $x.

Given that tax rate is 2.5% or 0.025

Then sales tax is given by product of 0.025 and x.

which is 0.025x.

Given that tax paid is $1.60 so both must be equal

$0.025x=1.6$

divide both side by 0.025

$x=1.6/0.025$

$x=64$

Hence final answer is $64.

7 0

1 year ago

Two times the quantity of seven less than one-fourth of a number is equal to fout

djverab [1.8K]

The unknown number is 108.

Step-by-step explanation:

Step 1:

Assume the unknown number is x.

We create an equation from the given data.

One-fourth of the number is $\frac{1}{4} x$ , seven less than one-fourth of the number is $\frac{1}{4} x -7$ . Two times the quantity of seven less than one-fourth of a number is therefore $2(\frac{1}{4} x -7)$ .

One-third of the number is $\frac{1}{3} x$ , four more than one-third of the number is given by $\frac{1}{3} x + 4$ .

Step 2:

We substitute both equations to determine the value of x.

$2(\frac{1}{4} x -7) = \frac{1}{3} x + 4.$

$(\frac{2}{4} x -2(7)) = \frac{1}{3} x + 4.$

$\frac{1}{2} x -14 = \frac{1}{3} x + 4.$

$\frac{1}{2} x - \frac{1}{3} x = 4+14 = 18.$

$\frac{1}{6} x = 18.$

$x= 6(18) = 108.$

So the unknown number is 108.

6 0

2 years ago

A circus ring is the arena where much of the action takes place at a circus. The figure below shows a circus ring with the cente

Goshia [24]

Answer:

Step-by-step explanation:

a) A diameter is a line that cuts a circle through at the centre. Line AD is a diameter.

Radius is half of a diameter i.e AD/2 = AO or OD

Chord is a straight line that touches the circumference of a circle. It doesn't pass through the centre like the diameter but cuts through the segments of a circle. Example of a chord is line FH

A tangent is a line that touches the circumference of a circle at just a point. It can touch any point on the circle. Example of a tangent line are AB and DE.

b) We must know that angle at a point or in a circle is 360°.

<EOH + <ECH = 360°

If <EOH = 131°

<ECH = 360° - 131°

<ECH = 229°

- <EFH falls in the circumference of the circle. Also know that, angle at the centre of a circle is twice angle at the circumference. Since <EOH is at the centre of the circle. <EFH = <EOH/2

<EFH = 131/2

<EFH = 65.5°

c) Given AB = DE, then <AB = <DE (oppositely directed angle).

Given <AOB = 20° then <DE = 20°

d) According to the diagram, <GFD = <GLD

If <GFD = 126°, then <GLD = 126°

e) Given HK = x+4, FK = x+14, GK = x, CK = x+32

From the diagram, CG = CK + KG

CG = x+32+x

CG = 2x+32

Also, FH = FK+HK

FH = x+14+x+4

FH = 2x+18

4 0

1 year ago

Triangle R S Q is shown. Angle R S Q is cut by perpendicular bisector l through point S and through midpoint T. The length of li

Nataly_w [17]

Answer:

RT = 8

Step-by-step explanation:

The given parameters for the triangle are;

The vertices of the given triangle = RSQ

The point on the perpendicular bisector = Pont S and T

The length of the line segment RT = x

The length of the line segment TQ = 8

The length of the line segment QS = 10

The length of the line segment RS = 10

Given that I is a perpendicular bisector that passes through the vertex S, we have;

The line I bisects the segment RQ at point T into equal segments TQ and TR

Therefore, TQ ≅ TR and we have TQ = TR = 8

TR = 8

TR = RT (reflexive property)

Therefore; RT = 8.

3 0

1 year ago

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The hypotenuse of a 45 -45 -90 triangle measures 128 cm what is the length of one leg of the triangle

erma4kov [3.2K]

This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.

4 0

2 years ago

Read 2 more answers